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      <JournalTitle>International Journal of Engineering, Science and</JournalTitle>
      <Volume-Issue>Volume 6, Issue 4</Volume-Issue>
      <Season>August 2017</Season>
      <ArticleType>Engineering, Science and Mathematics</ArticleType>
          <FirstName>Jada Prathap Kumar</FirstName>
          <FirstName>Jawali Channabasappa Umavathi** and Channakeshava</FirstName>
      <Abstract>In this present article, the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis Number, modified diffusivity ratio, Vadasz number and normalized porosity parameter on the stability of the system is investigated .The analysis reveals that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via buoyancy effect coupled with the conservation of nanoparticles to the thermal energy equation being a second –order effect. Stationary and oscillatory modes of convections have been studied. It is found that the critical thermal Raleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy, by the presence of the nanoparticles .Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution. The linear stability analysis is based on normal mode technique, while for nonlinear theory is based on the truncated representation of Fourier series method. A weakly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt numbers is investigated by a solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.</Abstract>
      <Keywords>Nanofluid, Porous medium, Instability, Natural convection.</Keywords>
        <Abstract>https://ijesm.co.in/ubijournal-v1copy/journals/abstract.php?article_id=3290&amp;title=LINEAR AND NONLINEAR ANALYSIS OF THERMAL INSTABILITY IN A POROUS SATURATED BY A NANOFLUID</Abstract>